Comparison tests Use the Comparison Test or the Limit Comparison Test to determine whether the following series converge.
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- 05* Let p, q> 0. Find the relation of p and q so that the following series is convergent. p>1 and p=1,q>1 p1 p1 and p=1, q<1 8 n=1 1 n²(Inn)arrow_forward00 Does the seriesE(- 1n+12+n° n4 converge absolutely, converge conditionally, or diverge? n= 1 Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. The series converges absolutely per the Comparison Test with > 00 n4 n= 1 B. The series diverges because the limit used in the Ratio Test is not less than or equal to 1. OC. The series converges conditionally per the Alternating Series Test and the Comparison Test with n= 1 D. The series converges absolutely because the limit used in the nth-Term Test is E. The series diverges because the limit used in the nth-Term Test does not exist. O F. The series converges conditionally per the Alternating Series Test and because the limit used in the Ratio Test isarrow_forwarddetermine if series is convergence or divergent and identify which test you usearrow_forward
- select the correct answer and explain step by steparrow_forwardUse any method to determine if the series converges or diverges. Give reasons for your answer. 00 (n+4)! n=1 4/nl4 Σ Select the correct choice below and fill in the answer box to complete your choice. OA. The series converges because the limit used in the nth-Term Test is OB. The series converges because the limit used in the Ratio Test is OC. The series diverges because the limit used in the nth-Term Test is OD. The series diverges because the limit used in the Ratio Test is Next qarrow_forwardFind the interval of convergence for the given power series. (x - 4)" Σ n(- 9)" n=1 The series is convergent from x = left end included (enter Y or N): to x = right end included (enter Y or N): M C ㅈ # $ A de L % 5 6 D 8 7 8 9 #arrow_forward
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- Use any method to determine if the series converges or diverges. Give reasons for your answer. 8 Σ (3e)="n2 n=1 Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) O A. The series diverges because the limit used in the Ratio Test is OB. The series converges because the limit used in the nth-Term Test is O c. The series converges because the limit used in the Ratio Test is SO D. The series diverges because the limit used in the nth-Term Test isarrow_forwardQUICK CHECK 2 Verify that the Ratio Test is inconclusive for E What test could be applied to show that Σ 1 converges? k2 k=1arrow_forwardt K Suppose a power series converges if |3x-6) ≤33 and diverges if |3x-615 33. Determine the radius and interval of convergence ICO The radius of convergence is R = Find the interval of convergence. Select the correct choice below and fill in the answer box to complete your choice OA. The interval of convergence is {x x=} (Simplify your answer. Type an exact answer.) B. The interval of convergence is (Simplify your answer. Type an exact answer Type your answer in interval notation.)arrow_forward
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